Note on the Lower semicontinuity with respect to the Weak Topology on W^{1,p}(Omega)

Abstract

We prove that the integral functional with the integrand g(x,u(x)) is lower semicontinuous with respect to the Weak Topology on W^{1,p}(Omega) if and only if g is convex in the second variable.

Keywords

• Lower semicontinuity
• Weak Topology